The Patriots moved quickly to counter the move, signing former Rams receiver Danny Amendola to a five-year contract worth $31 million, of which $10 million is guaranteed, according to a league source.

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Amendola, 27, is 4½ years younger than Welker, 2 inches taller, and more athletic after the catch, similar to Julian Edelman (also a free agent). But Amendola, who had a career-best 85 catches in 2010, has missed 20 games the past two seasons because of injury. Welker missed a total of three in his past eight seasons.

Why did it come to a divorce between Welker, who was beloved by fans and teammates, and the Patriots?

In the end, it was about respect. Welker never thought the Patriots showed enough. Bill Belichick, Robert Kraft, and everyone else associated with the team always spoke of Welker in the highest regard — and they meant those words. But when it comes to athletes, a team shows its true level of respect in dollars — and the Patriots never quite did that with Welker.

It looked as though it was finally going to happen this offseason. Despite trying to prove they could live without Welker early last season, the Patriots gained a new-found respect for his performance as he was the rock in a high-powered passing offense that lost tight ends Rob Gronkowski and Aaron Hernandez, and Edelman for long stretches of the season.

Welker led the NFL in catches (672) and yards (7,459) since 2007, his first season with the Patriots. He is the only receiver in league history to post five 100-catch seasons, and he and Andre Johnson of the Texans are the only ones to have 18 games with 10 or more receptions. Welker stands as the Patriots’ career leader in receptions.

There were good vibes all around at the end of the 2012 season. Welker felt wanted again, and the Patriots talked as if they would have a future together. Both sides felt it was a matter of when and not if Welker would re-sign with the Patriots, especially after Brady redid his contract and freed up $15 million against the salary cap for the next two seasons.

One of the few possible hangups, however, was whether the Patriots would expect Welker to take a discount after playing for the $9.515 million franchise tag in 2012.

And that’s exactly what happened.

The Patriots’ first offer this offseason came in much lower than Welker imagined at two years and $10 million plus incentives. That told Welker two things: His value in the Patriots’ eyes hadn’t changed, and it was time to look for another team.

The Patriots probably thought their offer, if combined with the tag — which they didn’t figure he would play for because he would agree to an extension — was more than acceptable at three years and $19.5 million guaranteed.

The Patriots could have had Welker for the same deal through 2014 — if not a little less — last offseason. But they didn’t do the deal last July, and they expected Welker to give them that discount in any event. But in Welker’s mind, he had to risk his career playing on that one-year tag. Why should he give the team a discount on that now?

In the end, the Patriots expected Welker to pay for their mistake of last offseason, with the help of a down market for free agent receivers. He declined to do that.

But Welker needed to find another team. As of Wednesday morning, there was no market for him; the Patriots appeared to have gauged the market perfectly. The Broncos previously expressed no interest in Welker. Members of their front office didn’t think Welker would be a good fit; they wanted to get better at the tight end position instead.

Perhaps that was a smokescreen, because Broncos sources said many in the front office thought Welker would be a perfect fit — and signing him could weaken a fellow AFC contender at the same time. Team president John Elway might have played possum so the Patriots would think there were no competitors for Welker.

Whether it was a planned deception or not, the Broncos were in perfect position to land Welker if he felt scorned by the Patriots. He did, and both sides quickly pushed toward a deal.

The Patriots made one last push to retain Welker, as Kraft talked to the receiver personally. The Patriots did not make a counter-offer, so the decision for Welker was easy. He was off to play with two very good outside threats in Demaryius Thomas and Eric Decker — something he never had in New England — and another Hall of Fame-bound quarterback in Manning.

You have to wonder how all of this sits with Brady, who despite his enormous clout with the Patriots does not get involved in personnel decisions. Brady and Welker were close friends and vacationed together, but Brady has had this happen before with Lawyer Milloy and Deion Branch. There’s no doubt, however, that Brady will miss Welker.

“I played with a lot of great players, whether that was Kevin Faulk or Randy Moss or Rodney Harrison, but Wes has been truly the greatest teammate you could possibly have,” Brady told the Globe in January. “His commitment to the team, his selflessness . . .

“When Wes clears out on a route, he clears out the route better than anybody I’ve ever seen. He knows he’s not getting the ball, but he almost takes as much pride in that as he does on the 6-yard option route to get open. That’s everything you need to know about Wes.

“That’s the best part about him. Whatever you need me to do, that’s what he’s going to do. He does it every day in practice, and I feel that’s what has always set him apart.”

With Welker gone, Belichick and offensive coordinator Josh McDaniels can move forward with an offense that we saw glimpses of early last season — one they feel will make them tougher to defend, especially in the playoffs.

With Welker, Gronkowski, and Hernandez, the Patriots had too many weapons that worked best in the middle of the field.

Removing Welker should leave the middle to the tight ends, with Hernandez taking most of Welker’s snaps inside the numbers. They could also use the other tight ends, Jake Ballard and Michael Hoomanawanui, more with Gronkowski to free up Hernandez as a receiver.

Amendola, who played for McDaniels in St. Louis, and a re-signed Edelman would be outside the numbers, running a variety of short passes, bubble screens, and crossing routes.

The real key to taking the offense to the next level is finding a dynamic boundary receiver with similar traits to Randy Moss. Barring a trade for a Larry Fitzgerald type, the Patriots will have to find that player in the draft.

They have a terrible track record, but it’s time for them to deliver their first consistent receiver in the draft since 2002 (Branch, David Givens). DeAndre Hopkins (Clemson), Justin Hunter (Tennessee), Keenan Allen (Cal), Terrance Williams (Baylor), and Markus Wheaton (Oregon State) are among those who have that type of potential.

The Patriots, through an unnecessarily messy endgame, have made their decision to move on from Welker, and they have a plan that makes the team better. Now it’s up to them to execute it.